Dilute antiferromagnetism in magnetically doped phosphorene

Abstract

We study the competition between Kondo physics and indirect exchange on monolayer black phosphorous using a realistic description of the band structure in combination with the density matrix renormalization group (DMRG) method. The Hamiltonian is reduced to a one-dimensional problem via an exact canonical transformation that makes it amenable to DMRG calculations, yielding exact results that fully incorporate the many-body physics. We find that a perturbative description of the problem is not appropriate and cannot account for the slow decay of the correlations and the complete lack of ferromagnetism. In addition, at some particular distances, the impurities decouple forming their own independent Kondo states. This can be predicted from the nodes of the Lindhard function. Our results indicate a possible route toward realizing dilute anti-ferromagnetism in phosphorene.

Spatial structure of correlations around a quantum impurity at the edge of a two-dimensional topological insulator

“…We have applied the Lanczos transformation method combined with the DMRG [35][36][37] , to study the many-body ground state of a quantum (S = 1/2) impurity (modeled as an Anderson impurity) coupled to the edge of a zigzag nanoribbon of stanene, a slightly buckled (non-planar) honeycomb lattice of Sn atoms, which hosts a topologically protected metallic edge state. The main motivation was to study the detailed spatial structure of the spin correlations between the quantum impurity and the electrons in the host, which characterize the Kondo ground state.…”

“…In order to perform unbiased numerical simulations of the model just described to calculate spin-spin correlations, we use the so-called block Lanczos method recently introduced by the authors 36,37 (see also Ref. 39 for an independent development of the same ideas).…”

“…II we present the model and a very brief description of the numerical method used (for details the reader is referred to previous papers by the authors [35][36][37] ). In Sec.…”

A Numerically Exact Approach to Quantum Impurity Problems in Realistic Lattice Geometries

“…The single impurity mapping can be used to study Kondo physics on graphene [79] or multi-band problems such as phosphorene, for instance [80]. It was found that, in the case of graphene, edge states tend to hybridize with the impurity spin introducing a competition between bulk and edge-induced Kondo screening.…”